Pore Network Investigation of Gas Trapping and Mobility During Foam Propagation Using Invasion Percolation with Memory

Abstract

Foam reduces the gas mobility in porous media both by increasing the effective viscosity of the gas phase and by trapping a large portion of the gas in place. This reduction is directly related to the number density of lamellae in the gas phase. Therefore, understanding the pore-level events associated with lamella generation and destruction processes and investigating the trapped foam behavior are of great importance in modeling foam mobility. In this paper, a pore network model based on the statistical physics method of invasion percolation with memory (IPM) is developed to simulate foam propagation as a drainage process of gas invasion into a porous media initially saturated with a surfactant solution. During this process, lamella generation, destruction, and mobilization are involved. This study sets out to explore the roles of pore level events that lead to foam destruction. To do so, static lamella destruction by capillary suction at the plateau borders is modeled using the Reynolds equation for film thinning and lamella rupture is assumed to occur when the film thickness falls below a certain critical thickness (hfc) at which the maximum disjoining pressure (Πmax) is attained. This mechanism is incorporated in the pore network model to which we add a notional time dependency of the invasion percolation with memory mechanism. Flowing lamellae are assumed to rupture at a fixed limiting capillary pressure (Pcap ) lower than Πmax. Results show that a critical regeneration probability (freg ) is required for the generation of strong foam in the network. The mobilization pressure gradient depends on both the number of lamellae in the flow path and the sizes of the throats that make up of this path. At the same freg, the mobilization pressure gradient markedly decreases after incorporating lamella destruction mechanism. The structure of the displacement pattern of the invading phase at breakthrough changes under the competition between capillary and yield stress-like forces. During transient foam displacement, gas saturation increases, and foam texture becomes finer with increasing freg. The flowing foam fraction increases much more slowly with pressure gradient after accounting for the viscous friction associated with the flow in the already open paths. Comparison with experiments shows that current pore network model can capture the main features of the transient foam flow in porous media.